Range Estimation of a Moving Target Using Ultrasound Differential Zadoff-Chu Codes

TL;DR

This paper introduces differential Zadoff-Chu sequences for ultrasound-based range estimation of moving targets, significantly improving accuracy and robustness under Doppler effects and low SNR conditions.

Contribution

It proposes a novel DZC signal design and a reduced-complexity ranging algorithm that outperform traditional ZC-based methods in dynamic environments.

Findings

Over 90% range estimates within 1.6 mm error at -10 dB SNR

Achieves RMSE less than 0.76 mm at 10 dB SNR for short-range movement

Maintains RMSE below 7.70 mm for larger ranges and higher velocities

Abstract

High accuracy range estimation is an essential tool required in many modern applications and technologies. However, continuous range estimation of a moving target is a challenging task, especially under Doppler effects. This paper presents a novel signal design, which we name differential Zadoff-Chu (DZC). Under Doppler effects, DZC sequences improve the performance of the maximum likelihood (ML)-based range estimation compared to its performance when using regular ZC sequences. Moreover, a reduced-complexity ranging algorithm is proposed utilizing DZC sequences and is shown to outperform the regular ZC ML-based range estimation. The proposed system is evaluated in a typical indoor environment, using low-cost ultrasound hardware. Under a low signal to noise ratio (-10 dB SNR), more than 90% of the range estimates are in less than 1.6 mm error, with a movement range from $0.2$ m to 2.2 m and a maximum velocity of 0.5 m/s. For the same movement range, the system provides range estimates with a root mean square error (RMSE) less than 0.76 mm in a high SNR scenario (10 dB), and an MSE less than 0.85 mm in a low SNR scenario (-10 dB). For a larger movement range from 1.8 m to 4.2 m with a maximum velocity of 1.91 m/s, the proposed system provides range estimates with RMSE less than 7.70 mm at 10 dB SNR.